Welcome and good luck on a difficult project As one of the V.K. builder in here, I can tell you (and others also) that this is a much more complicated project than meets the eye.
Looking forward to your build!

The first mechanical challenge that I've had is figuring out the mechanism use for extending the arm, I couldn't tell if a screw drive was being used or maybe a flexible metal rod spooled out (like in automatic radio antenna on cars). I think I finally solved it, after re-watching Leon's interview and it also answered the question I had of the purpose of the smaller rod (bent at 90 degrees) attached to the arm.
The smaller rod is attached to the belt of the pulley system and that drives the rod out.
The image I was trying to include displays way to big
I also uploaded a video of my proof of concept test at https://youtu.be/5WaR8gv0kBU
Thanks to everyone for your support and a special thank you to Joberg - I've taken an immense amount of inspiration from your amazing build._________________If only you could see the things I've seen with your eyes.

The first mechanical challenge that I've had is figuring out the mechanism use for extending the arm, I couldn't tell if a screw drive was being used or maybe a flexible metal rod spooled out (like in automatic radio antenna on cars). I think I finally solved it, after re-watching Leon's interview and it also answered the question I had of the purpose of the smaller rod (bent at 90 degrees) attached to the arm.
The smaller rod is attached to the belt of the pulley system and that drives the rod out.
The image I was trying to include displays way to big
I also uploaded a video of my proof of concept test at https://youtu.be/5WaR8gv0kBU
Thanks to everyone for your support and a special thank you to Joberg - I've taken an immense amount of inspiration from your amazing build.

Thanks for the praises Tom Yes, you're right, that side rod made it possible (as you've discovered) to extend the arm. When I emailed Mike Fink, he mentioned that the travel of the arm was minimal:
One, the main rod (attached to the eye) is traveling under the main aluminum piece and stops at the rectangle box (that contains the motor for the driving pulley), that's why it was impossible to extend that rod, or to have it moving with a screw drive mechanism.
Two, the side rod (the one that you've shown on YouTube) is driven by the driving pulley, the other pulley is a dummy one.

The other motor (the one moving the eye) is in the piece attached to the main rod and placed in the middle of it and the eye.
Hope that helps

Joberg - yes that information is a great help, thanks for confirming what I suspected. I hope to have the lift, extend and rotation mechanisms done by the end of the week (they'll just be skeletal until I can build up the the rest of it)._________________If only you could see the things I've seen with your eyes.

I must admit that I never really thought to look on ebay for those parts. Never expected that anyone made them so I just thought I'd make them myself.
For the bar graph below the smaller screens I'm using:https://www.digikey.com/product-detail/en/lite-on-inc/LTA-1000HR/160-1066-ND/153273 . I have 3 of them on hand from a prior project and they seem to match the dimensions I'm using based on the white buttons being 1.5cm (and they look like the same ones from ebay that you linked to - unexpected coincidence ). Haven't yet seen a bar graph of 8 green, 4 red - LED's so hoping to make it from individual rectangular LED's or surface mount LED's using light pipes.
Screens do seem a big challenge - not finding quite the right sizes in LCD or TFT, just have to keep looking (would be great to find CRT's the right size).
Currently testing if the torque of the servo motors I have are strong enough to lift the arm._________________If only you could see the things I've seen with your eyes.

That red bar seems alright Tom. As for the buttons (the 3 lit white ones at the right hand side of the big screen), the measurement seems o.k. too. (gotta check mine to make sure...I'm at work at the moment).

Screen are going to be a challenge to be sure, and as you know, they will dictate, once and for all, the whole machine look/measurement

As for the arm, it shouldn't be a problem moving the rod/eye combo. The only movement the eye was incapable of doing was pivoting on its axle.

Let me explain: the eye is folded into the trench at the rear of the V.K. (if you look straight at the rear, the trench is on the right hand side).
The only travel that piece is capable of doing is the up/down motion...Michael Fink and the other prop makers working on that project were not able (time most likely) to make the eye pivot.

For that reason, the only movement you'll see in the movie is the up/down motion of the eye piece. Hope it helps.